J Mater Sci(2006)41:7425-7436 parallel-beam assembly (PW1710 based). The data SEM. Surface preparation for the EBSD sample is were recorded for 20 values from 40 to 154 using Cu critical since the diffraction information originates in a Kan radiation with a step size of 0.05 and a 3-s scan 20 nm layer at the surface, corresponding to the pen time per step. The lower limit of 40 was chosen to etration depth for back-scattered electrons. In our ensure a constant irradiated volume for all data. The process, the sample surface was polished, etched, and integrated intensities for all reflections were calcu- ultrasonically cleaned before EBSD examination. The lated using PhILLIPs APD software EBSD data were collected sequentially by positioning The March-Dollase function [28, P,(n), was used to the focussed electron beam on each grain individually estimate the probability of observing diffraction from The normal to the sample surface was tilted 70 to the the hkl planes at a given angle incident beam and the eBsd pattern was captured at a beam voltage of 20 kV. The individual crystal orien Pr(n)=(cos2n+r-lsin2n)-3/2 (2) tations were analyzed using commercial software to generate discrete pole figures for each localized where n is the angle between the basal plane(001) and microtexture data se the(hkl) planes. The parameter r is the ' compaction ratio'(final thickness/initial thickness) in the original March model. For the present purpose, r was used to Results and discussion indicate the degree of texture: r= l for a random sample and r< 1 for a textured sample. The March- Texture control in c-axis TA interlayers Dollase function satisfies the following normalized equation (29] A cross-section of gel-cast green tape is shown in Fig. 1 and demonstrates alignment of the alumina seed platelets by the gel casting process. Good alignment of Phk(n,中) sin dude=2 (3) the seed alumina platelets is a key factor in attaining high particle packing density in the green bodies, and the aligned, high aspect ratio platelets did not prevent where Phkl(l, o)is the polar axis density function, o is ially and cold-isostatically pressed compacts. High the in-plane rotation angle, and n is the tilt angle about sintered densities were ob ainable the TA samples an axis in the plane of diffraction and perpendicular to after sintering at 1550C for 2 h, despite the pres the is g axis. P(n), is therefore a multiple of the ran- of the aligned platelets and the limitations of dom distribution(MRD)in an isotropic polycrystal In sureless sintering. As expected, under the same the present case of axisymmetric texture Eg 3 simp sintering conditions lower final densities were associ fies to ated with higher initial platelet contents Phkl(n)sin ndn After normalizing the polar density function Pnkdn) 多3 and fitting the March-Dollase function, the oriented volume fraction was calculated as the volume fraction of crystallites oriented in directions for which P>I F (greater than random). The oriented volume fraction was thus defined as: Oriented=/(P(m)-1)sin ndn where is given by P(1)=1. Fig. 1 SEM image of a cross-section of gel-cast textured green Microtexture was also investigated using electron tape showing the distribution of seed platelets(marked by back-scatter diffraction(EBSD) in the LEO 982-FEG- arrows)in the tap 2 Springerparallel-beam assembly (PW1710 based). The data were recorded for 2h values from 40 to 154 using Cu Ka1 radiation with a step size of 0.05 and a 3-s scan time per step. The lower limit of 40 was chosen to ensure a constant irradiated volume for all data. The integrated intensities for all reflections were calcu￾lated using PHILLIPS APD software. The March–Dollase function [28], Pr(g), was used to estimate the probability of observing diffraction from the hkl planes at a given angle: PrðÞ¼ð g r 2 cos2 g þ r
1 sin2 gÞ
3=2 ð2Þ where g is the angle between the basal plane (001) and the (hkl) planes. The parameter r is the ‘compaction ratio’ (final thickness/initial thickness) in the original March model. For the present purpose, r was used to indicate the degree of texture: r = 1 for a random sample and r < 1 for a textured sample. The March– Dollase function satisfies the following normalized equation [29] Z 2p 0 Zp=2 0 Phklðg;/Þsin gdgd/ ¼ 2p ð3Þ where Phklðg; /Þ is the polar axis density function, / is the in-plane rotation angle, and g is the tilt angle about an axis in the plane of diffraction and perpendicular to the is / axis. Pr(g), is therefore a multiple of the ran￾dom distribution (MRD) in an isotropic polycrystal. In the present case of axisymmetric texture Eq. 3 simpli- fies to Z p=2 0 PhklðgÞsin gdg ¼ 1 ð4Þ After normalizing the polar density function Phkl(g) and fitting the March–Dollase function, the oriented volume fraction was calculated as the volume fraction of crystallites oriented in directions for which P > 1 (greater than random). The oriented volume fraction was thus defined as: Voriented ¼ Z g1 0 ðPðgÞ
1Þsin gdg ð5Þ where g1 is given by P(g1) = 1. Microtexture was also investigated using electron back-scatter diffraction (EBSD) in the LEO 982-FEG￾SEM. Surface preparation for the EBSD sample is critical since the diffraction information originates in a 20 nm layer at the surface, corresponding to the pen￾etration depth for back-scattered electrons. In our process, the sample surface was polished, etched, and ultrasonically cleaned before EBSD examination. The EBSD data were collected sequentially by positioning the focussed electron beam on each grain individually. The normal to the sample surface was tilted 70o to the incident beam and the EBSD pattern was captured at a beam voltage of 20 kV. The individual crystal orien￾tations were analyzed using commercial software to generate discrete pole figures for each localized, microtexture data set. Results and discussion Texture control in c-axis TA interlayers A cross-section of gel-cast green tape is shown in Fig. 1 and demonstrates alignment of the alumina seed platelets by the gel casting process. Good alignment of the seed alumina platelets is a key factor in attaining high particle packing density in the green bodies, and the aligned, high aspect ratio platelets did not prevent the achievement of high green densities in the uniax￾ially and cold-isostatically pressed compacts. High sintered densities were obtainable in the TA samples after sintering at 1550 C for 2 h, despite the presence of the aligned platelets and the limitations of pres￾sureless sintering. As expected, under the same sintering conditions lower final densities were associ￾ated with higher initial platelet contents. Fig. 1 SEM image of a cross-section of gel-cast textured green tape showing the distribution of seed platelets (marked by arrows) in the tape 7428 J Mater Sci (2006) 41:7425–7436 123